Method of using unbalanced alternating electric field in microfluidic devices

ABSTRACT

The applicant describes a new method of generating directed motion of the liquid in the microfluidic device by applying “un-balanced” AC electric field for generating electroosmosis and related hydrodynamic flow in the chamber with any symmetry of the elements, including spherical or cylindrical symmetry, and any relative position of these elements. Direction of the flow depends on the phase of the “un-balanced” electric field, which opens a simple way to operate flow and create a desirable flow pattern.

FIELD OF THE INVENTION

This invention describes a method for generating directed relativemotion of liquid in microfluidic device by applying uniform alternatingelectric field with “unbalanced” time dependence to the system of thecharged micro-obstacles that experience non-linear polarization in theapplied electric field, which causes non-linear electro-osmosis.

BACKGROUND OF THE INVENTION

Electric field influence on the charged surfaces generates relativemotion of the phases in heterogeneous systems. In the case of“electrophoresis”, particles or macromolecules move relative to theliquid, whereas in the case of “electroosmosis”, liquid moves relativeto the solid matrix. These “electrokinetic phenomena” are known for 200years and are the basis of several important technologies. One of therecent important technological developments exploiting these phenomenais “microfluidics”, which is technology of operating motion of the smallvolumes of liquid. There is a version of mocrofluidic devices that useselectroosmosis as driving force initiating liquid motion. There areseveral reviews describing current level of microfluidic development: 1.“Microfluidics: Basis Issues, Applications and Challenges”, by H. A.Stone and S. Kim, AIChE Journal, vol. 47, 6, pp. 1250-1254, 2001; 2.“Micro Total Analysis Systems. Introduction, Theory and Technology”, byD. R. Reyes, D. Iossifidis, P. A. Auroux, A. Manz, Anal. Chem, 74,2623-2636, 2002; 3. “Flexible Methods for Microfluidics”, by G. W.Whitesides and A. D. Stroock, Physics Today, 42-48, June 2001.

All devices that employ this effect can be considered as combination ofmaterial objects, such as electrodes, canals, valves, etc, and electricfield. Accordingly, there are three approaches to achieve specifiedgoals:

-   -   either to arrange material objects at certain appropriate design        and order    -   or apply electric field with appropriate properties.    -   or use both ways together.

U.S. Pat. No. 5,976,336 “Microfluidic devices incorporating improvedchannel geometries” by R. S. Dubrow, C. B. Kennedy, L. J. Bousse, 1999,might serve as an example of the first approach. In this patent we donot consider material construction of the microfluidic device at all.

In this patent we are dealing exclusively with the second approach.

In the general, electric field strength E is characterized withfrequency ω, amplitude A and phase ψ as following:E(x, t)=A(x, t) sin(ωt+ψ)  (1)

-   -   where x and t are some space coordinate and time respectively.

There are two modes of the electric field depending on the frequency:

-   -   DC field at the zero frequency    -   AC field at non-zero frequency

The first and most used version is DC field. There are several USPatents dealing with this type of electrokinetic microfluidic devices:by S. J. Salvatore, U.S. Pat. No. 4,908,112 “Silicon semiconductor waferfor analyzing micronic biological samples” in 1990; by P. K. Dasgupta,U.S. Pat. No. 5,660,703 “Apparatus for capillary electrophoresis havingan auxiliary electroosmotic pump” in 1997, by J. W. Parce, U.S. Pat. No.6,394,759 “Micropump” and U.S. Pat. No. 6,012,902 “Micropump” in 2000,by Kopf-Sill, U.S. Pat. No. 6,617,823 “Systems for monitoring andcontrolling fluid flows rates in microfluidic systems” in 2003.

This mode of the electric field has a big disadvantage of beingassociated with Faraday current on electrodes. This current is relatedto electrochemical reactions on electrodes. These reactions generatechemical species, which could cause contamination.

It is possible to prevent, or at least to minimize this contaminationmanaging design of material objects as it is suggested, for instance, byP. K. Dasgupta, U.S. Pat. No. 5,660,703 “Apparatus for capillaryelectrophoresis having an auxiliary electroosmotic pump” in 1997.

Replacing DC field with AC field offers much simpler solution to thisproblem. In this mode of the electric field, it is possible to eliminateelectrochemical reactions completely if frequency is high enough.

However, application of the AC field requires a special means forcreating directed motion of the liquid. Just regular linearelectroosmosis in symmetrical system does not generate the directedmotion of liquid and useless for pumping. This problem could be resolvedby introducing asymmetry into the system. This idea is widely known inthe generating directed motion of the particles by AC electric field.Non-uniformly spaced AC electric field with the space coordinate xdependent amplitude generates directed motion of the particles known as“dielectrophoresis”. There is a large bulk of literature ondielectrophoresis. One of the most recent patents on this subject is byF. F. Becker, P. R. C. Gascoyne, Y. Huang and X. B. Wang, U.S. Pat. No.6,641,708 “Method and apparatus for fractionation using conventionaldielectrophoresis and field flow fractionation”, 2003.

The same idea can be introduced for generating directed motion of theliquid. Space dependence of the AC electric field amplitude A(x) isinduced by special arrangements of electrodes. Application of this ideato the microfluidics is described in the several recent papers: by A.Ajdari “Pumping liquids using asymmetric electrode arrays”, PhysicalReview E, vol. 61, 1, pp. 45-48, 2000, by A. B. D. Brown, C. G. Smith,and A. R. Rennie “Pumping of water with ac electric fields applied toasymmetric pairs of microelectrodes”, Physical Review E, vol. 63,016305, 2000.

This approach to the microfluidic pumping is complicated by the problemof the changing direction of the liquid motion. Asymmetry of thematerial objects in the device determines this direction. It means thatsuch devices could pump liquid only in one direction. Voltage modulationsuggested by A. Ajdari “Pumping liquids using asymmetric electrodearrays”, Physical Review E, vol. 61, 1, pp. 45-48 introduces a constant,time independent component of the current, which constituents return tothe DC field with all related problems.

In addition, it might be hard to control asymmetry of the elements onthis small scale of dimensions.

In this patent we evoke an old idea expressed many years ago in Russianliterature for eliminating linear effects in electrophoresis withpurpose of investigating non-linear components of electrophoreticmotion. It was suggested by S. S. Dukhin, A. K. Vidybida, A. S. Dukhinand A. A. Serikov “Aperiodic Electrophoresis. Directed drift ofdispersed particles in a uniform anharmonic alternating electric field”,Kolloidnyi Zh., vo. 49, 5, 752-755, 1988, English.

Instead of the asymmetry of the material object, this idea suggests touse a special time dependence of the electric field, keeping itsamplitude uniform, space independent. This type of electric field iscalled “un-balanced”. It does not have constant, time independentcomponent. This eliminates linear effects, Faraday current, preventspossible contamination by electrochemical reactions residue. At the sametime it generates directed motion of the particles, which depends on thenon-linear terms in electrophoretic mobility. There is a generaldefinition of this field and some examples given in the detaileddescription of this patent.

This idea has never been before suggested for electroosmosis and relatedmicrofluidic applications.

BRIEF SUMMARY OF INVENTION

The applicant describes a new method of generating directed motion ofthe liquid in the microfluidic device by applying “un-balanced” ACelectric field for generating electroosmosis and related hydrodynamicflow in the chamber with any symmetry of the elements, includingspherical or cylindrical symmetry, and any relative position of theseelements. Direction of the flow depends on the phase of the“un-balanced” electric field, which opens a simple way to operate flowand create a desirable flow pattern.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1. Two examples of the “un-balanced” AC electric field.

DETAILED DESCRIPTION OF INVENTION

Microfluidics is rather new discipline with a purpose of creating newmeans for operating motion of liquid on very small scales of hundredsmicrons and below. Microfluidics is closely linked to electrokinetics,which is scientific discipline regarding various phenomena that occur inthe heterogeneous systems under influence of electric field. Inparticular, electrokinetic effect of electroosmosis is of great interestfor microfluidics because it could be defined as motion of the liquidgenerated by the electric field influence on interfacial electriccharges.

Electroosmosis is closely related to electrophoresis, which is motion ofthe solid particles relative to the liquid induced by the externalelectric field.

These electrokinetic phenomena are known for almost 200 years with mostattention paid to electrophoresis in both experimental and theoreticalaspects. Some of this knowledge could be transferred and expanded nowfrom electrophoresis to electroosmosis for microfluidics relatedpurposes.

Both effects are characterized with a speed of the motion. In the caseof electrophoresis it is motion of particle relative to the liquidV_(eph), in the case of electroosmosis it is opposite, motion of liquidrelative to the immobile solid phase V_(eo). In the imaginary case ofthe collection of the separate particles in the liquid, speed ofelectrophoresis is equal to the speed of electroosmosis in magnitude butopposite in sign, because they are simply different due to thedifference in the immobile frame of reference.V_(eo)=−V_(eph)  (2)

In the classical electrokinetic theory (see Dukhin, S. S. and Derjaguin,B. V. “Electrokinetic Phenomena” in “Surface and Colloid Science”, E.Matijevic (Ed.), John Wiley & Sons, NY, v. 7 (1974)) electrophoresis andelectroosmosis are linear effects in regard to the electric fieldstrength. It happens because external field electric potential dropassociated with a small colloidal particle 2Ea is much less than typicalpotential in the particles double layers RTIF≈25 m V. Here a is particleradius, R is a gas constant, T is absolute temperature, F is Faradayconstant. This usually expressed as the following non-equality:$\begin{matrix}{\frac{EFa}{RT} < 1} & (3)\end{matrix}$

For particle with 1 micron radius this restrict E to be below 250 V/cm.The typical value of electric field strength in classicalelectrokinetics is below 10 V/cm, which explains why electrophoresis andelectroosmosis are assumed to be linear with electric field strength. Aspecial notion of “electrophoretic mobility” as coefficientproportionality between speed of electrophoresis and electric fieldstrength has been introduced:V _(eph)=μ_(eph) E  (4)

About 2 decades ago it became clear that assumption of linearity doesnot work in some cases. The notion of “non-linear electrophoresis” wasintroduce. Review of these earlier works was given by S. S. Dukhin, A.K. Vidybida, A. S. Dukhin and A. A. Serikov “Aperiodic Electrophoresis.Directed drift of dispersed particles in a uniform anharmonicalternating electric field”, Kolloidnyi Zh., vo. 49, 5, 752-755, 1988,English. The speed of non-linear electrophoresis contains two terms,classical linear and term proportional to the third power of theelectric field strength:V _(eph) =μ _(eph) E+μ _(eph,3) +E ³  (5)

Importance of the non-linear term depends on the value of the non-linearelectrophoretic mobility μ_(eph,3). There were theories developed forgeneral non-conducting particles and for two special cases when thisparameter is particularly large: 1) porous charged particles such asionite or polyelectrolyte; 2) metal ideally polarized particles.

For general non-conducting particles (oxides, latex, pigments, etc)non-linear term is related to the polarization of the double layercaused by surface conductivity. There is a dimensionless parametercalled “Dukhin number”, (see Lyklema, J., “Fundamentals of Interface andColloid Science”, vol. 1-3, Academic Press, London-NY, (1995-2000),which determines the magnitude of this effect. This number isreciprocally proportional to the particle size. In the case ofmicrofluidics the size of obstacles is rather large, certainly exceedingmicron. This leads to the small Dukhin number, negligible double layerpolarization and small, even hardly measurable non-linearelectrophoretic term if obstacles are made from non-conducting material.

For the purpose of this patent the most important is the case of metalparticles. Non-linear electrophoresis is the most pronounced in thiscase. The non-linear term in this case is related to the difference inconductivities between particle and liquid.

Theory of non-linear electrophoresis of metal ideally polarizedparticles was developed by A. S. Dukhin “Biospecific mechanism of doublelayer formation and peculiarities of cell electrophoresis”, Colloids andSurfaces A, 73, pp. 29-48, 1993. He derived the following expression forthis effect: $\begin{matrix}{V_{eph} = {{\frac{ɛ_{m}ɛ_{o}\zeta}{\eta}E} - {\frac{9ɛ_{m}ɛ_{0}a^{2}}{8\eta\quad C_{dl}}\left( \frac{\partial C_{dl}}{\partial\phi} \right)_{\phi = \zeta}E^{3}}}} & (6)\end{matrix}$

-   -   where ε_(m) and ε₀ are dielectric permittivities of media and        vacuum, η is dynamic viscosity, φ is electric potential, C_(dl)        id double layer capacitance, ζ is electrokinetic potential of        particles, which is measure of their equilibrium electric        charge.

This simple theory can be directly used for estimating speed of theliquid flow in the microfluidic device with collection of the metalelectrodes for generating electroosmotic flow under influence of DCelectric field. There is just one difference. Instead of particlesmoving relatively to the liquid, liquid moves relatively to the fixedcylindrical or spherical electrodes. $\begin{matrix}{V_{eo} = {{- V_{eph}} = {{{- \frac{ɛ_{m}ɛ_{0}\zeta}{\eta}}E} + {\frac{9ɛ_{m}ɛ_{0}a^{2}}{8\eta\quad C_{dl}}\left( \frac{\partial C_{dl}}{\partial\phi} \right)_{\phi = \zeta}E^{3}}}}} & (7)\end{matrix}$

This expression allows us to compare linear and non-linear effects. Forinstance, it turns out that for particle size 10 microns, non-linearterm becomes larger than linear term at the electric field strengthexceeding only approximately 25 V/cm. In the case of 100 micronsparticles this critical field is only 2.5 V/cm.

These simple approximate calculations indicate that non-linearelectroosmosis could be used as a basis for microfluidic device. It isvery fortunate because it opens way to replace DC field with AC field.This replacement is desirable very much because it allows to eliminateFaraday current and related contamination by products of electrochemicalreactions.

In order to determine the optimum way to apply AC electric field weagain turn our attention to the existing theory of electrophoresis.

Fifteen years ago a group of Ukrainian scientists suggested to useso-called “un-balanced” AC electric field for eliminating linear term inthe speed of the particle motion and creating particle drift with thespeed that depends only on the non-linear mobility: S. S. Dukhin, A. K.Vidybida, A. S. Dukhin and A. A. Serikov “Aperiodic Electrophoresis.Directed drift of dispersed particles in a uniform anharmonicalternating electric field”, Kolloidnyi Zh., vo. 49, 5, 752-755, 1988,English.

The definition of the “un-balanced” electric field could be given in theform of the following two equations: $\begin{matrix}{{\int_{0}^{T}{E{\mathbb{d}t}}} = 0} & (8) \\{{\int_{0}^{T}{E^{3}{\mathbb{d}t}}} \neq 0} & (9)\end{matrix}$

The first equation means that there should be no time independentcomponent of the current in the system. The second one is required forretaining the non-linear term in the particle drifting motion. FIG. 1shows 2 examples of “un-balanced” AC electric field. The top exampleillustrates the following AC field, which is sum of two harmonicsshifted by certain phase:E=E ₁ sin(ωt)+E ₂ sin(2ωt+Ψ)  (10)

If we would apply electric field like this to the real dispersion,particle start to drift with the speed that depends on the non-linearmobility only. Consequently, in the case of microfluidic device, liquidwould exhibit drifting motion with the following speed: $\begin{matrix}{V_{eo}^{drift} = {{\frac{1}{T_{e}}{\int_{0}^{Te}{V_{eo}{\mathbb{d}t}}}}\quad = {{\frac{3}{4}\mu_{{ef},3}E_{1}^{2}E_{2}\sin\quad\psi} = {\frac{27}{32}\frac{ɛ_{m}ɛ_{0}a^{2}}{\eta\quad C_{dl}}\left( \frac{\partial C_{dl}}{\partial\phi} \right)_{\phi = \zeta}E_{1}^{2}E_{2}\sin\quad\psi}}}} & (11)\end{matrix}$

-   -   where T_(e) is the time period of the electric field.

Direction of the motion depends on the phase shift between harmonics.This gives an easy way to operate with liquid motion.

There is infinite number of the various “un-balanced” AC electricfields. We just showed only two examples on the FIG. 1. This fields mustsatisfy conditions (8) and (9) and there is also certain restrictions ofthe frequency.

First of all, frequency must be above critical frequency of Warburgimpedance ω_(W) in order to eliminate Faraday current. It is usuallyseveral KHz.

Secondly, frequency must be below Maxwell-Wagner frequency ω_(MW) thatdepends mostly on conductivity of the liquid K_(m), (see Dukhin, S. S.and Shilov V. N. “Dielectric phenomena and the double layer in dispersedsystems and polyelectrolytes”, John Wiley and Sons, NY, (1974)):$\begin{matrix}{{\omega ⪡ \omega_{MW}} = \frac{K_{m}}{ɛ_{m}ɛ_{0}}} & (12)\end{matrix}$

This frequency characterizes relaxation of the double layer.Polarization charges that cause non-linear effect require some time todevelop completely. This condition specifies Maxwell-Wagner frequency.For conductivity of liquid K_(m)=0.01 S/m, this critical frequencyequals roughly to 2.2 MHz.

Third condition requires frequency to be below frequency of theelectroosmotic field relaxation ω_(eo):${\omega ⪡ \omega_{eo}} = {\frac{v}{D}\omega_{MW}}$

-   -   where v is kinematic viscosity of the liquid, D is effective        diffusion coefficient of the electrolyte.

This condition reflects the fact that electric field should change intime slow enough for allowing electroosmotic flow to develop completelywithin the double layer. This restriction is not essential in aqueoussystems where because kinematic viscosity exceeds diffusion coefficientseveral order of magnitude. This means that this frequency is muchlarger than Maxwell-Wagner frequency.

However, there is one more important frequency of hydrodynamic nature.Electroosmotic flow establishes quickly itself within the thin DoubleLayer. This flow makes liquid to move beyond the double layer. It takessome time for this bulk flow to develop. This critical time depends onthe size of the object that generates initial electroosmotic flow.Corresponding frequency of this hydrodynamic relaxation ω_(h) is givenas following: ${\omega ⪡ \omega_{h}} = \frac{v}{a^{2}}$

This hydrodynamic relaxation limits available frequency range verysubstantially in the case of microfluidics. The larger size of theelectroosmosis generating obstacles the lower this frequency becomes.For instance, for 100 micron generating electrodes it is only about 0.1KHz. This means that for large microfluidic device obstacles of hundredsmicrons in size, it is practically impossible to take advantage of allbenefits related with AC field. Hydrodynamic flow would not havesufficient time to develop completely if frequency high is enough toeliminate Faraday current.

It looks like the size of the electroosmosis generating obstacles shouldnot exceed 10 microns. Hydrodynamic relaxation frequency correspondingto this size is about 10 KHz. This opens the frequency window betweenWarburg frequency ω_(W) (several KHz) and hydrodynamic relaxationfrequency ω_(h) (about 10 KHz).

1. Method of generating directed motion of liquid by applyingun-balanced alternating electric field, which is AC electric field witha zero time averaged component and finite time averaged of the higherthan one powers of the electric field strength, to the system ofmaterial objects with arbitrary symmetry for inducing electroosmoticflow on the object-liquid interfaces.
 2. Method of the claim 1, whereinthe frequency of the AC electric field exceeds Warburg frequency of theseveral KHz for eliminating Faraday current but is lower thanhydrodynamic relaxation frequency
 3. Method of the claim 1, wherein theelectroosmosis generating objects have either spherical or cylindricalsymmetry and size not exceeding 10 microns.
 4. Method of the claim 1,wherein the system of electroosmosis generating objects is microfluidicsdevice with array of the metal electrodes.
 5. Method of the claim 1,wherein the system of electroosmosis generating objects is microfluidicsdevice with array of the metal obstacles and electric field is appliedby the means of external electrodes systems.